Is #f(x)= cos(x+(pi)/4) # increasing or decreasing at #x=pi/3 #?

1 Answer
Shwetank Mauria
Nov 5, 2016

#f(x)=cos(x+pi/4)# is decreasing at #x=pi/3#

Explanation:

Whether a function is increasing or decreasing at a point depends on the value of its derivative at that point.

If derivative is positive, function is increasing and if it is negative, function is decreasing.

As #f(x)=cos(x+pi/4)#, #f'(x)=-sin(x+pi/4)#.

and at #x=pi/3#, #f'(pi/3)=-sin(pi/3+pi/4)=-sin((7pi)/12)=-sin(pi-(5pi)/12)=-sin((5pi)/12)#.

As #sin((5pi)/12)>0# (#(5pi)/12# being acute angle), #f'(pi/3)<0#

Hence, #f(x)=cos(x+pi/4)# is decreasing at #x=pi/3#

Related questions
See all questions in Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
Impact of this question
2608 views around the world
You can reuse this answer
Creative Commons License